Which of the following rectangular hyperbola has eccentricity equal to $\sqrt{2}$

x y = 100

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x y = 98

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x y = 0.8

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x y = 1

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Solution

The correct option is D $x y = 1$
The eccentricity of rectangular hyperbola is constant and equal to $\sqrt{2} .$ Hence, it is independent of value of $c$ .

All the given rectangular hyperbola has same eccentricity.

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Similar questions

Q. Assertion :Eccentricity of rectangular hyperbola

x y = c^{2}

\sqrt{2}

. Reason: The transverse & conjugate axes of rectangular hyperbola are equal.

Q. Assertion :A hyperbola whose asymptotes are at right angles to each other is called rectangular hyperbola. Reason: Eccentricity of rectangular hyperbola is

\sqrt{2}

Which of the following statements are correct?

1. The particular kind of hyperbola in which the lengths of the transverse and conjugate axis are equal is called an equilateral hyperbola.

2. Eccentricity of equilateral hyperbola = $\sqrt{2}$
3. Equation of pair of asymptotes of rectangular hyperbola $x^{2} - y^{2} = a^{2}$ is $x^{2} - y^{2} = 0$

4. Equation of pair of asymptotes of rectangular hyperbola $x^{2} - y^{2} = a^{2}$ is $x^{2} - y^{2} = - a^{2}$

Q. A hyperbola passes through

(1, 2)

and has asymptotes as

x + y - 2 = 0

and

7 x + y - 8 = 0

. Eccentricity of hyperbola is equal to

Q. The length of Transverse axis and Conjugate axis is always equal in rectangular hyperbola and its eccentricity is always

\sqrt{2}

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Which of the following rectangular hyperbola has eccentricity equal to √2

The correct option is D xy=1The eccentricity of rectangular hyperbola is constant and equal to √2. Hence, it is independent of value of c. All the given rectangular hyperbola has same eccentricity.

Which of the following rectangular hyperbola has eccentricity equal to $\sqrt{2}$

The correct option is D $x y = 1$
The eccentricity of rectangular hyperbola is constant and equal to $\sqrt{2} .$ Hence, it is independent of value of $c$ .

All the given rectangular hyperbola has same eccentricity.